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There is strong evidence that the 11 March 2011 Tohoku earthquake rupture reached the seafloor. This is surprising because the shallow portion of the plate interface in subduction is thought to be frictionally stable, leading to the widely held view that coseismic rupture would stop several ten of thousands of kilometers downdip of the seafloor. Various explanations have been proposed to reconcile this seeming inconsistency, including dynamic weakening (e.g., thermal pressurization) and extreme stress release around shallow subducted seamounts. We offer a simpler explanation supported by 2D dynamic rupture simulations of the Tohoku earthquake. Our models account for depth-dependent material properties and the complex geometry of the fault, seafloor, and material interfaces, based on seismic surveys of the Japan Trench. The fault obeys rate-and-state friction with standard logarithmic dependence of shear strength on slip velocity in steady state. In our preferred model, the uppermost section of the fault is velocity strengthening. Rupture nucleates on a deeper, velocity-weakening section. Waves released by deep slip reflect off the deafloor, transmitting large stress changes to the upper section of the fault driving the rupture through the velocity-strengthening region to the trench. We validate the model against seafloor deformation and 1-Hz Global Positioning System (GPS) data. The seafloor displacements constrain the seismogenic depth and overall amount of slip, particularly near the trench. Our simulations reproduce many features in the GPS data, thereby providing insight into the rupture process and seismic wave field. Sensitivity to parameters is explored through an extensive suite of simulations. Neither static seafloor deformation nor onshore 1-Hz GPS data can uniquely determine near-trench frictional properties due to trade-offs with average stress drop. While conducted specifically for the Japan Trench region, our simulations suggest that rupture to the trench in megathrust events is quite possible, even if velocity-strengthening properties extend tens of kilometers landward from the trench.